Terry Gou, the Taiwanese tycoon whose company makes most of Apple Inc.’s iPhones, donned his lucky yellow scarf and headed into the headquarters of Sharp Corp. in Osaka, Japan. It was time for a last-ditch bid to take over the fabled but floundering Japanese electronics firm.

At the time of the Jan. 30 meeting, the prospects of a deal—such as the one officially announced Wednesday—were dim as Japanese media were reporting that Mr. Gou’s company, Foxconn Technology Group, didn’t stand a chance against a Japanese government-backed...

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